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Martin said Scholtens was a respected QC who had worked in public and administrative law for 36 years.

She was Crown Counsel at the Crown Law Office for 10 years and previously worked as a solicitor privately and in several government departments. Since 1996 she has practiced public law from the independent bar, and in 2002 was made Queen's Counsel.

She has been involved in or carried out many inquiries including acting as Counsel Assisting the 2004 Commission of Inquiry into Police Conduct. In 2003 she carried out a review of the operation of the Protected Disclosures Act 2000 for the Minister of State Services.

If, at the conclusion of the inquiry, deficiencies are found in the appointment process, the Prime Minister will seek advice from the Solicitor General or the State Services Commissioner on the appropriate next steps.

Earlier this week Jacinda Ardern said she was "hugely frustrated" more information about Haumaha - which was unknown at the time of his promotion to deputy police commissioner - becoming public after the appointment was made.

A new inquiry chair has been announced for the inquiry into Assistant Commissioner Wallace Haumaha. Photo /File

Her comments came after an ongoing Herald investigation into the promotion revealed three women working on a joint project walked out of Police National Headquarters because of alleged bullying by Haumaha.

The policy analysts, two from the Justice Ministry, one from Corrections, were based at PNHQ in Wellington working in the Maori, Pacific, Ethnic Services division run by Haumaha, a superintendent at the time.

The cross-sector project aimed to improve "justice outcomes" for Maori.

Alleged verbal bullying contributed to the women leaving PNHQ in June 2016, feeling "devalued and disillusioned".

The trio told their managers, did not return to PNHQ, and continued working on the project from the Justice Ministry offices. Haumaha did not respond to a request for comment

"I'm hugely frustrated to be in a situation where an appointment has been made and now we're having information being drip-fed out, which should have been made available at the time of the appointment," the Prime Minister said.

Two senior government ministers assured Parliament the scope of the inquiry was wide enough to consider the bullying allegations.

Grant Robertson also said the chief executives of the Justice Ministry and Corrections, Andrew Bridgman and Ray Smith respectively, would be asked how the bullying allegations were handled.

Conflicting accounts have emerged about what followed.

Corrections has said there was no record of alleged bullying.

But "issues were raised" about the management of the project, according to the Justice Ministry.

"The issues around behaviour were raised at the highest level between the acting chief executive of the ministry, Audrey Sonerson, and Deputy Commissioner of Police Mike Clement," said deputy chief executive Colin Lynch.

"The ministry expected police to follow up this issue appropriately."

But the police say an allegation of bullying was made to Clement by a "third party, external to all agencies".

"Clement immediately made contact with the Ministry of Justice and the Department of Corrections to request more information and advise that the staff involved could make a complaint if they wished."

But with no formal complaint, or more information, the matter could go no further.

One of the three women who walked out of the justice project now plans to make a formal complaint about Haumaha's alleged behaviour.

She said the trio had raised the matter with their respective managers, she was never asked to make a formal complaint, and the women had believed their managers would handle that.

The inquiry into Haumaha's appointment was announced the day the Herald revealed comments he made during Operation Austin, an investigation into historic police rape allegations made by Louise Nicholas.

He described his friends Brad Shipton as a "softie" and Bob Schollum as a "legend" with women, while one officer told the 2004 investigation into the police sex allegations that Haumaha described Nicholas' allegations as "a nonsense".

While Haumaha has apologised, Police Minister Stuart Nash said he was unaware of the "deeply disappointing" comments when he gave Haumaha's name to the Prime Minister for the deputy commissioner role.

But the inquiry is yet to start, more than seven weeks after it was announced by Acting Prime Minister Winston Peters.

Haumaha's ties with New Zealand First have also dogged the inquiry - overseen by Internal Affairs Minister Tracey Martin, a NZ First MP - although the Prime Minister Jacinda Ardern downplayed any suggestions of a conflict of interest.